Definitely apply for a provisional, do check if anything's notifiable to the DVLA.
NB, they have very woolly wording, autism is only notifiable IF it affects your ability to drive lots of people have been caught out with that one and denied a provisional because they declared their autism despite it not affecting their driving. If in doubt see your GP and ask before you submit anything.
My DD has similar Dx and started in a manual without me disclosing her disabilities as she didn't want anyone to know.
After 30, yes THIRTY lessons, despite me asking if she was doing okay and her instructor telling me she was fine after every lesson, her instructor asked to see me and told me she couldn't use her feet independently on the pedals, every time she pressed the clutch, she pressed the brake as well and she was out of ideas about how to help her.
So we decided an auto would be so much easier to manage, as well as full disability disclosure to the instructor.
DD had 2 instructors for her auto driving lessons, one was brilliant but 2 weeks before DD's test had to stop teaching as she had to claim benefits. DD was of course thrown by that and cancelled her test.
It took a few goes to find another suitable auto instructor, one man turned up in a car emblazoned with disability logos and a large sign on the top which said Disability something or other and she was mortified and wouldn't even get in it.
She didn't want a male instructor and finding a female instructor for an auto wasn't easy.
At last we found one but out of our area, we had to meet in the nearest town. She was clueless about autism and didn't give simple enough instructions so DD found it very hard work. She caught up to her former standard, was 2 weeks from taking her test, again. At the next lesson, her instructor messed her around for her lesson time, texting and changing it 3 times in an hour so DD was in pieces with stress, arrived for the lesson, instructor said something to her before she got into the car, DD had a meltdown and was sobbing, instructor yelled at her, I walked over to cancel the lesson and take DD straight home, instructor yelled at me that my DD was only making a scene because she was a spoilt brat who couldn't get her own way.
DD was in pieces again and cancelled her test. I'd already paid the instructor for it but she refused to refund me.
Massive lesson there, make sure the instructor understands how to interact with pupils with autism.
DD's always had fatigue but since then it's got worse and she was dxd with CFS and hasn't yet had the energy to drive again. BUT she was perfectly capable in an automatic car with a good instructor and wants to take it up again as soon as she feels she is able to.
Her first auto instructor was amazing, she asked me to sit in on some lessons so DD could get used to passengers talking while she was driving. I asked if she thought DD needed any adaptations to a vehicle and she said not.
I have no doubt that DD could have passed her test on both of those occasions and been a good driver.
She passed the written test with flying colours.
At that time, DD was on indefinite DLA and also had a Blue Badge. Now on PIP enhanced both rates after Tribunal and still has the BB. I looked into Motability and for her circumstances thought it was a more expensive way of driving. I bought a small old auto for her for £2K to learn in and have ended up using it as our main car.
You asked about adaptations, there is a centre that assesses disabled drivers and recommends adaptations, www.drivingmobility.org.uk/our-services/driving-assessments/